(Lack of the) Role of Gravity in Fluid Pipes

[justadream]

TPR SW Passage 23 #7


“In a straight pipe of uniform cross-sectional area filled with a nonviscous, incompressible fluid, the pressure at one end is equal to the pressure at the other end. Which of the following statements is/are true?



I. The volume flow rate is zero because there is no net force on the fluid

II. The volume flow rate is constant throughout the pipe because the cross-sectional area is uniform

III. The pipe is not inclined relative to the horizontal since the pressure is constant.

Answer: II and III and only.

Why is II correct? What if you had a pipe vertically oriented and open to the atmosphere? The pressure differential at the top and bottom would be the same (assuming this pipe isn’t like…..500m long). But wouldn’t gravity act to accelerate the fluid’s movement and thus increase the flow rate?

---

Members don't see this ad.

 

[t5Nitro]

TPR SW Passage 23 #7


“In a straight pipe of uniform cross-sectional area filled with a nonviscous, incompressible fluid, the pressure at one end is equal to the pressure at the other end. Which of the following statements is/are true?



I. The volume flow rate is zero because there is no net force on the fluid

II. The volume flow rate is constant throughout the pipe because the cross-sectional area is uniform

III. The pipe is not inclined relative to the horizontal since the pressure is constant.

Answer: II and III and only.

Why is II correct? What if you had a pipe vertically oriented and open to the atmosphere? The pressure differential at the top and bottom would be the same (assuming this pipe isn’t like…..500m long). But wouldn’t gravity act to accelerate the fluid’s movement and thus increase the flow rate?

II is correct because you have a straight pipe with uniform cross-sectional area. The pressure at one end is equal to the pressure at the other end. At the same height and same pressure, velocity of the fluid is also unchanged (look at Bernoulli's equation here). The 'Av' volume flow rate is therefore the same everywhere in the pipe. I'm not sure what you're asking when you are hypothetically flipping the pipe vertically.

 

[DrknoSDN]

II. The volume flow rate is constant throughout the pipe because the cross-sectional area is uniform
III. The pipe is not inclined relative to the horizontal since the pressure is constant.

Answer: II and III and only.

Why is II correct? What if you had a pipe vertically oriented and open to the atmosphere? The pressure differential at the top and bottom would be the same (assuming this pipe isn’t like…..500m long). But wouldn’t gravity act to accelerate the fluid’s movement and thus increase the flow rate?

The real question is why you would ask why 2 is true when your example the pipe is oriented vertically and choice III says it is oriented perfectly horizontally.

Choice III says that the pipe must be horizontal to have constant pressure. Gravity would cause a pressure difference because the deeper you measure in the fluid the more fluid there is pressing down creating pressure. Also "(assuming this pipe isn’t like…..500m long)" isn't a good assumption. Even with a short pipe you could still measure a pressure difference. With just a 3 meter pipe you would measure a gauge pressure equal to 0.1 atm using water. Just think of a pool/lake, if you swim down you need to pop your ears because the pressure changes so rapidly.